Langmuir 1996, 12, 5399-5406
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Amorphous Carbons: Surface Structure and Adsorptive Properties L. E. Cascarini de Torre and E. J. Bottani Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA), Casilla de Correo 16, Sucursal 4, RA-1900, La Plata, Argentina
W. A. Steele* Chemistry Department, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802 Received March 14, 1996. In Final Form: July 17, 1996X Bernal’s model is employed to represent the structure of amorphous carbonaceous materials. The adsorptive properties corresponding to this model surface are tested by means of Monte Carlo computer simulations. Nitrogen, oxygen, and carbon dioxide are the adsorbates studied at different temperatures and surface coverages. Molecular cross-sectional areas are estimated from the simulations and the results compared with values in the literature. The simulated configurations of the adsorbed molecules are discussed as well as the variation with coverage of their tilt angle distributions and their density profiles as a function of distance from the surface. Integral heats of adsorption have also been evaluated and discussed.
1. Introduction It is well-known that the behavior of an adsorbed molecule depends on the properties of both the solid surface and the adsorbate itself. Among the most relevant characteristics of the solid are its chemical nature, its topography, and the presence of impurities. For the adsorbate it is important to consider molecular size, shape, and electronic configuration. It has also been shown that temperature, or more precisely, the thermal energy of the adsorbate, and the lateral interactions are factors from which a balance is established that defines the thermodynamic properties of the adsorbed phase. These questions have been most often studied theoretically and by simulation for homogeneous solid surfaces such as the graphite basal plane or other perfect single-crystal surfaces. However there is similar work concerned with heterogeneous surfaces which is mainly oriented toward measuring or assessing the nature of the heterogeneity.1-3 Perhaps the most difficult part of this problem resides in the fact that the structure of real heterogeneous surfaces cannot easily be modeled. In previous papers the authors have proposed the use of Bernal’s model to represent the surface structure of carbonaceous materials.4,5 It has been shown that this model is capable of reproducing the isotherms and heats of adsorption of several simple gases adsorbed on several heterogeneous solids. In this paper, the adsorption of nitrogen, oxygen, and carbon dioxide on the Bernal surface representation of amorphous carbon is simulated at different temperatures using the grand canonical (GCMC) and canonical (CEMC) ensembles. The results that will be discussed here include the average cross-sectional areas of these gases and their X
Abstract published in Advance ACS Abstracts, October 1, 1996.
(1) Ross, S.; Olivier, J. P. On Physical Adsorption; Interscience Publishing: New York, 1964. (2) Rudzinski, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992. (3) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (4) Cascarini de Torre, L. E.; Bottani, E. J. Langmuir 1995, 11, 221. (5) Cascarini de Torre, L. E.; Flores, E. S.; Llanos, J. L.; Bottani, E. J. Langmuir 1995, 11, 4742.
S0743-7463(96)00246-6 CCC: $12.00
dependence on temperature and surface coverage, the density profiles of the adsorbed phase as a function of the distance of the adsorbate molecule from the surface, the heats of adsorption, and the average configurations and tilt angles of the adsorbed molecules. 2. Interactions and Surface Model It is here assumed that the structure of a heterogeneous carbon black can be described by the Bernal model. This model has been successfully employed previously to describe argon adsorption on the bare and hydroxylated TiO2 surface.6,7 A detailed description has been given elsewhere.4,5 Briefly, it represents the atoms of a noncrystalline solid by spheres which are randomly closepacked. As an adsorbent surface, the spheres are then taken to be sites which interact with an adsorbate molecule via Lennard-Jones 12-6 functions with parameters usually chosen to fit the experimental data in the limit of low coverage (Henry’s Law regime).5 The model can be criticized because it does not deal with the variable coordination number produced by the chemical bonding between the atoms that constitute the solid. In spite of this problem it was shown4 that the model can be made to represent the adsorptive properties of the surfaces of both carbonaceous and oxide materials, provided that both the model and real solids have the same atomic density. In this approximation, the adsorbate molecules are modeled as collections of sites that interact with the sites in neighboring adsorbate molecules and with the sites of the Bernal model of the solid. Explicit values of the parameters of the various site-site interactions needed in the present study are listed in ref 4 together with the well-depth and size parameters for the adsorbateadsorbate sites obtained from studies of the bulk phases that have been reported in the literature. Quadrupolequadrupole interactions for nitrogen and carbon dioxide have been included using a discrete charge representation of the quadrupole moment. (6) Bakaev, V. A.; Steele, W. A. Langmuir 1992, 8, 148. (7) Bakaev, V. A.; Steele, W. A. Langmuir 1992, 8, 1379.
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The computer simulation algorithms have been described elsewhere8,9 and need no further description. Molecular configurations on the surface have been obtained from CEMC simulations in which equilibrium films were generated by taking 6 × 106 attempted moves for the first point in each run and (2-4) × 106 attempted moves for other points. The analysis of orientations is based on at least 400 equilibrated configurations over which averages are taken. GCMC simulations were performed to obtain the isotherms and the density profiles of the adsorbed film in the direction perpendicular to the surface. The adsorption isotherms have been compared with experiment in order to check the interaction parameters used in the simulations as well as the specific BET surface area. The adsorbent used in this simulation was constituted by a cube containing 1000 spherical sites and periodic boundary conditions in the dimensions parallel to the surface. It had a geometrical area of 12.68 nm2. The number of adsorbed molecules employed in the CEMC simulations was varied from 5 up to 500. On geometric grounds, it is estimated that the monolayer capacity on this surface should be about 70 N2 molecules. 3. Results and Discussion Simulations were performed at temperatures above and below the normal boiling point of each of the three gases used in order to show the effect of thermal energy upon the configurations and average orientations of the adsorbate molecules. At temperatures well below the normal boiling point it is expected that the adsorbed molecules will be highly ordered. The simulations show how this order is affected by the heterogeneity of the Bernal surface and how it changes as temperature is increased. The monolayer densities, which are affected by changing molecular orientations as well as thermal expansion, were also evaluated. Thus, nitrogen adsorption was simulated at 50.0, 77.5, and 90.0 K, oxygen was studied at 50.0, 80.2, 90.0, and 100.0 K, and carbon dioxide was studied at 120.0, 150.0, 194.7, and 230.0 K. 3.1. Density Profiles. In Figure 1, the dependence of the local density upon distance from the surface is shown for different numbers of nitrogen molecules adsorbed on the model amorphous carbon black at two temperatures: part a, 77.5 K; part b, 50 K. In these figures, F(Z) is the number of molecules per unit area in a distance range dZ at distance Z away from the surface, divided by dZ. The profiles shown in Figure 1a correspond to those expected for adsorption on a heterogeneous surface. The atomic roughness of the substrate has broadened the sharp peaks that are often seen for adsorption on the graphite basal plane.4 Also, the layer structure is minimal for those molecules that are more distant than the second layer. This is not unexpected, since the temperature of these simulations is high enough to give liquid-like multilayer films. In contrast, it can be seen in Figure 1b that adsorption at 50.0 K mostly produces a layered film at least up to the fifth layer even though the substrate is atomically rough. It appears that these films are solid, with a layer or two of surface-melted material on the outside. The density profiles in Figure 2 are for oxygen adsorption at two surface coverages, with part a corresponding to 50 K and part b to 80.2 K. In general, the N2 and O2 profiles are very similar except for the fact that multilayer formation begins at lower surface coverages in the case (8) Bottani, E. J.; Bakaev, V. A. Langmuir 1994, 10, 1550. (9) Bottani, E. J.; Bakaev, V. A.; Steele, W. A. Chem. Eng. Sci. 1994, 49, 2931.
Figure 1. (a) Density profiles for nitrogen at 77.5 K. The number of adsorbed molecules is 5-500. (b) Density profiles for nitrogen at 50 K. The number of adsorbed molecules is 5-500. Here, σ ) 3.36 Å.
of oxygen adsorption. This is related to the somewhat larger area per molecule for O2. As can be seen in Figure 3, carbon dioxide adsorption proceeds in a different way from that of O2 and N2. Only at very low surface coverages it is possible to distinguish the first and second layers. When the number of adsorbed molecules increases to 300, a liquid-like multilayer film forms. This behavior is observed even at the lowest temperature studied (120 K), where a roughly layer-bylayer regime might be expected. Similar profiles have been obtained for CO2 adsorption on the basal plane of graphite but only for coverages corresponding to two layers or less (Figure 4 in ref 9). Another feature of these profiles is that CO2 molecules in the first layer are closer to the surface than N2 and O2 molecules. This will be addressed later on when the configurations of the adsorbed molecules are discussed. 3.2. N2, O2, and CO2 Cross-Sectional Areas. To determine the specific surface area of solids, the BET method is currently most often employed. It is generally accepted that it provides a good estimate of the monolayer capacity, at least when the BET C parameter is large (>100). A value for the molecular cross-sectional area of the adsorbate is also needed to complete the determination of surface area from monolayer capacity. It is known that the cross-sectional area of an adsorbate is somewhat dependent upon the chemical nature of the surface, its
Amorphous Carbons
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Figure 4. Oxygen cross-sectional area. Reference values taken from Smith,14 Brunauer,15 McClellan et al.,16 and Tildesley.12
Figure 2. (a) Density profiles for oxygen at 50 K. The number of adsorbed molecules is 90-200. (b) Density profiles for oxygen at 80.2 K. The number of adsorbed molecules is 100-500 and σ ) 3.38 Å.
Figure 3. Density profiles for carbon dioxide at 120 K. The number of adsorbed molecules is 10-300 and σ ) 3.14 Å.
homogeneity, and the temperature at which the isotherm is determined.9,10 In addition, the area occupied by an adsorbed molecule will change somewhat with surface (10) Bottani, E. J.; Llanos, J. L.; Cascarini de Torre, L. E. Collect. Czech. Chem. Commun. 1991, 56, 569.
coverage when the adsorbate can adopt different orientations relative to the surface. This leads to several possible values for the cross-sectional area of nonspherical adsorbate molecules. For example, values from 0.14 up to 0.205 nm2 have been proposed for CO2. In the case of N2, the proposed values range from 0.14 up to 0.24 nm2, and the values for O2 start at 0.135 nm2 and range up to 0.165 nm2.11 (These are the values proposed for adsorption on carbonaceous materials. Other values11 proposed for oxides, metals, and other solids have been ignored here.) To estimate the cross-sectional area of an adsorbate, several approaches have been proposed. The simplest one is based upon the adsorbed film density. Another method is based on a “calibration” based on measurements on a sample whose area has been determined by an independent and reliable method (such as electron microscopy or immersion calorimetry). There is still another possibility according to which the monolayer capacities obtained with the adsorbate under study are compared with those for a reference adsorbate whose cross-sectional area is considered to be better known. Finally, one can use the molecular size parameters used in the simulations (and elsewhere) to estimate the area per molecule. Taking N2 as an example, the size parameters give 0.374 nm as the distance of minimum interaction between side-by-side pairs and 0.484 nm as the distance between end-to-end pairs. If we assume that these dimensions are the relevant ones of a molecular area calculation, an isolated molecule that is perpendicular to the surface will have an area of 0.110 nm2, and the same molecule in a close-packed triangular array will occupy 0.121 nm2. If this molecule lies flat and is assumed to have the shape of a spherocylinder, it will occupy 0.121 nm2. The molecular arrangement in a close-packed monolayer is somewhat more problematic, but a herringbone array is believed to have the minimum energy configuration for linear quadrupolar molecules;13 in this case, one estimates the molecular area in a layer which has all molecules lying flat on the surface to be 0.148 nm2, depending upon the herringbone packing angle. Not surprisingly, both numbers are smaller than the accepted value for the N2 area, which corresponds to a thermally (11) Mikhail, R. Sh.; Robens, E. Microstructure and Thermal Analysis of Solid Surfaces; John Wiley and Sons: New York, 1983; Appendix C. (12) Joshi, Y. P.; Tildesley, D. J. Surf. Sci. 1986, 166, 169. (13) Steele, W. A. Langmuir 1996, 12, 145. (14) Smith, W. R.; Ford, D. G. J. Phys. Chem. 1965, 69, 3587. (15) Brunauer, S. J. Colloid Interface Sci. 1973, 45, 27. (16) McClellan, A. L.; Harnsberger, H. F. J. Colloid Interface Sci. 1967, 23, 577. (17) Karnaukhov, A. P. J. Colloid Interface Sci. 1985, 103, 311. (18) Ismail, I. M. K. Carbon 1990, 28, 423.
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Figure 5. Nitrogen cross-sectional area. Reference values taken from Karnaukhov,17 Ismail,18 and Ross and Olivier.1
Figure 6. Carbon dioxide cross-sectional area. Reference values taken from ref 11.
expanded, liquid-like layer at 78 K. In fact, if the molecule lies flat but rotates freely in-plane so as to appear circular with a diameter of 0.484 nm, it will occupy an area of 0.202 nm2 in a close-packed triangular array. The point here is that the area for a linear molecule of length/width ) 1.3 changes by 20% or more (depending upon the inplane orientational freedom) as the molecule in the monolayer rotates from surface-normal to surface-parallel. Since the most favorable orientations of linear molecules are parallel to the local surface plane (at least in the limit of low coverage), there is reason to suppose that these areas will depend upon surface roughness (small for the graphite basal plane, large for an amorphous surface such as that considered here). Furthermore, increasing the temperature produces not only thermal expansion but an approach of the molecular orientation toward the vertical in a closely packed monolayer. The simulated orientational distributions for the systems under study support these arguments but indicate that surface roughness has played an important role in blurring the simple picture presented here. In a computer simulation it is possible to record the coordinates of all adsorbed molecules. This allows one to assign molecules to a given layer without reference to BET or other approximate theory. Also of particular interest here are the angles that define the orientations of the adsorbed molecules. From these and the molecular sizes, which are calculated as indicated above from the σ and bond length for each molecule, projected crosssectional areas for a given tilt angle with in-plane rotational freedom can be calculated. Thus, during a CEMC simulation, every equilibrated configuration was used in a calculation of the most probable orientation for a molecule adsorbed in the first layer (see below). For each gas, Figures 4-6 show the values of the projected area of a molecule with the most probable orientation as a function of the number of adsorbed molecules. These figures also include values obtained from the literature for carbonaceous materials.11 It is important to note that the average projected cross-sectional area exhibits large variations near the point where the number of adsorbed molecules reaches the monolayer capacity. At higher surface coverages, the observed spread of the points is within the statistical error of the simulations. Another common feature for the three gases is that the region of surface coverage where the cross-sectional area is rapidly changing corresponds to the relative pressure range employed to determine the BET monolayer capacity. This may be the reason why several values for the crosssectional area have been proposed for these gases adsorbed
on different samples. At surface coverages near monolayer completion, the average orientation of a molecule in the first layer is determined by a number of factors: changes in the gas-solid interaction as the least favorable part of the surface becomes covered; an increase in the importance of the repulsive lateral interactions (i.e., crowding effects); and the effects of the beginning of adsorption in layers higher than the first upon the configurations of the molecules underneath such molecules. Monolayer capacity values can also be calculated directly from the CEMC simulations. For example, an integration over the first-layer peak in the curves of density versus distance for the surface yields the desired number of molecules in the first layer as a function of the total number of molecules on the surface. A comparison of these values with those estimated from the projected cross-sectional areas per molecule and the geometric area of the computer box showed that the two are in good agreement. In addition, GCMC simulations were performed to generate adsorption isotherms which were then used to determine the BET monolayer capacity. If these results are used together with the area of the simulation box, it is possible to use these monolayer capacities to calculate the BET molecular cross-sectional area for each adsorbate. The values obtained are in perfect agreement with the results shown in Figures 4-6. For example, the N2 monolayer capacities obtained in this way yield molecular areas of 0.173 nm2 at 90 K, 0.192 nm2 at 77 K, and 0.197 nm2 at 50 K. It is also interesting to compare the limiting values of the cross-sectional areas obtained from the simulations with the currently accepted values derived from the liquid and solid densities. At 80.2, 90, and 100 K, the oxygen cross-sectional area is very close to the value obtained from the liquid density. It could thus be concluded that the adsorbed phase is liquid-like in the range 80-90 K. At 50 K the limiting value is larger (ca. 0.17 nm2), which indicates the formation of a less dense adsorbed film, which is probably due to a change in the orientation of these adsorbed molecules. Several values have been proposed for the CO2 crosssectional area in a monolayer. The relevant ones are the ideal (0.164 nm2) and those derived from the densities of the solid (0.142 nm2) and liquid (0.179 nm2) phases. The limiting values obtained (Figure 6) at the lowest temperatures are close to the value deduced from the liquid density while, at temperatures higher than 194.7 K, the results agree with the cross-sectional area corresponding to the solid. 3.3. Configurations of Adsorbed Molecules. Although terms like first and upper layers are reasonably
Amorphous Carbons
Figure 7. Snapshot of carbon dioxide molecules in the first layer at 120 K. The total number of adsorbed molecules is 400: (a) top view; (b) side view. The size of the molecules is approximately to scale.
well defined for adsorption on single-crystal surfaces, the definition becomes somewhat arbitrary for the atomically rough heterogeneous surfaces modeled here. A molecule is considered to be in the first layer if it is located nearer to the surface than a distance estimated from the simulated density profiles. In the case of homogeneous surfaces, deep minima occur in the density profiles, indicating clear separations between layers. However, the minima are not so sharp for heterogeneous surfaces and thus this estimate of the limits between layers is less precise. Snapshots for configurations of adsorbed N2 at 77.5 K and CO2 at 120 K are shown in Figures 7 and 8. Both top views and side views are shown. The N2 snapshot is for 80 molecules, which is slightly larger than the number in the complete monolayer. In the picture for CO2 only the molecules located in the first layer are shown; in this case, the total number of adsorbed molecules is three times the monolayer value. The most important feature in these figures is that there is no in-plane orientational order of the adsorbed molecules to be seen and not much tilt-angle ordering, even at low temperatures. This indicates that the surface roughness of the Bernal solid is very important in determining the structure of the adsorbed phase. From configurations such as those shown, distributions of the tilt angles of the adsorbed molecules have been calculated. The distributions of cos θ, where θ is the angle between the molecular axis and the nominal surface plane, are shown for O2 at three temperatures, with the curves in Figures 9 and 10 corresponding to 250 and 500 adsorbed molecules, respectively. At 50 K the angular distributions for both coverages are still quite broad, in contrast to the situation for oxygen adsorbed on the basal plane of graphite, where these distributions tend to be sharp.19 For the first layer distributions in Figure 9, there is a significant change between 90 and 100 K with the molecules exhibiting more orientational order than in the (19) Bhethanabotla, V.; Steele, W. A. Can. J. Chem. 1988, 66, 866. (20) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon Press: New York, 1976.
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Figure 8. Snapshot of nitrogen molecules in the first layer at 77.5 K. The total number of adsorbed molecules ) 300: (a) top view; (b) side view. The size of the molecules is approximately to scale.
Figure 9. Distribution of tilt angles for adsorbed oxygen molecules at 50 K: (0) molecules in the first layer; (O) molecules in upper layers (mostly the second).
case of 50 K and with the ordering increasing as the temperature goes from 90 to 100 K. It appears that surface roughness is dominant at 50 K, but lateral interactions (crowding) become the determining factor as the temperature increases to 100 K. Nitrogen tilt-angle distributions (not shown here) exhibit behavior similar to that of oxygen except that the distributions are always narrower. At 77.5 K the differences between the distributions of N2 molecules in the first and in the upper layers are negligible. At 50 K the most probable tilt angle, at coverages higher that the monolayer, is approximately 73° while at 77.5 K it is 62°, finally reaching a value between 65° and 70° at 90 K. Carbon dioxide shows broad tilt-angle distributions at all temperatures (see Figures 12-15). At 120 and 150 K the most probable tilt angle is approximately 70°. In both cases there is a noticeable number of molecules lying either almost parallel to or almost vertical on the surface.
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Figure 10. Distribution of tilt angles for oxygen molecules at 90 K: (0) molecules in the first layer; (O) molecules in upper layers.
Figure 13. Distribution of tilt angles for carbon dioxide molecules at 150 K: (broken line) molecules in the first layer; (solid line) molecules in upper layers.
Figure 11. Distribution of tilt angles for oxygen molecules at 100 K: (0) molecules in the first layer; (O) molecules in upper layers.
Figure 14. Distribution of tilt angles for carbon dioxide molecules at 194.7 K: (broken line) molecules in the first layer; (solid line) molecules in upper layers.
Figure 12. Distribution of tilt angles for carbon dioxide molecules: T ) 120 K; (0) molecules in the first layer; (O) molecules in upper layers.
Figure 15. Distribution of tilt angles for carbon dioxide molecules at 230 K: (broken line) molecules in the first layer; (solid line) molecules in upper layers.
As temperature increases, the distributions become narrower and the difference between the first and the upper layers becomes less important. The average tilt angle is
ca. 60°. Note that the distributions show some sort of “tail” toward large tilt angles that is not observed for the other two gases.
Amorphous Carbons
Figure 16. Coverage dependence of the average potential energy of adsorbed oxygen. The surface coverage (in layers) is calculated with the monolayer capacity determined by the BET method at each temperature to be Nm ) 80 (50 K), 92 (80.2 K), and 91 (90 K). Note that the average potential energy is equal to the integral energy of adsorption from the ideal gas.20
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phase is liquid-like, as previously inferred from the crosssectional area analysis. At 50 K, the energy curve tends to a value that is greater that the vaporization enthalpy of the pure solid. The CO2 enthalpy curve at 230 K tends toward the enthalpy of the bulk liquid at 216.6 K (the triple point) and at 194.7 K but not at lower temperatures. The step observed at 120 K is very close to the sublimation enthalpy (25.1 kJ/mol), suggesting that the adsorbed phase is solid-like in the region of the monolayer completion. Considering the values of the cross-sectional area together with these results, it is clear that the adsorbed phase is less dense than the bulk at the lowest temperatures studied here. This could be explained if the effect of surface heterogeneity is taken into account. Gas-solid interactions determine the structure of the adsorbed phase. At low temperatures the surface is capable of orienting the adsorbate to produce configurations with molecules mostly lying parallel to the local surfaces. As temperature increases the adsorbate molecules acquire enough kinetic energy to begin to reorient, which then allows the formation of denser surface layers with increased (negative) lateral interaction energy. It is difficult to quantitatively compare these enthalpies of adsorption with experiment because the simulations yield integral enthalpies. Very precise results are needed to differentiate such curves to yield the differential enthalpies that are generally obtained experimentally.21 4. Conclusions
Figure 17. Same as Figure 16 but for carbon dioxide. The surface coverage is calculated with the monolayer capacity determined by the BET method at each temperature to be Nm ) 70 (120 K), 77 (150 K), 84 (194.7 K), and 87 (230 K).
3.4. Heats of Adsorption. The average molar potential energy of the adsorbed gases has been determined from the simulations as a function of the number of adsorbed molecules. Figures 16 and 17 show curves obtained for O2 and CO2 at different temperatures as a function of surface coverage. (The monolayer capacity at each temperature was determined by applying BET theory to the simulated isotherms.) The results for nitrogen do not show any striking feature. (The curve corresponding to 77.5 K has been published previously in a paper where the model was tested against experimental results.4) At 50 K the energy of the adsorbed film tends to a highcoverage value that is slightly greater than the vaporization enthalpy of the bulk, indicating that the structure in the film corresponds to a liquid or a less compact (amorphous?) solid. This agrees with the analysis of the cross-sectional area values. The shapes of the adsorption energy curves for the three gases agree with those expected for adsorption on a heterogeneous surface. The contribution of the lateral interaction energy to the energy of adsorption appears for CO2 in the region of monolayer completion only as a decrease in the slope of the curve relative to that expected for the gas-solid part of the interaction. Oxygen enthalpy curves for 80.2 and 90 K tend toward the vaporization enthalpy of the bulk liquid, confirming that the adsorbed
The isotherms for these systems increase smoothly with coverage (i.e., show no steps), as expected for a heterogeneous surface. Nevertheless it is possible to observe reasonably sharp layer formation (up to the fourth layer) in the density plot of Figure 1b for nitrogen at 50 K. In the case of carbon dioxide, an absence of layer formation is found even at 120 K. This was also observed in the simulations of the adsorption of this gas on the basal plane of graphite. Another feature is that carbon dioxide molecules are closer to the surface than nitrogen and oxygen molecules. This is a consequence of the tendency for all molecules to lie parallel to the surface in the monolayer. The carbon dioxide is longer than nitrogen or oxygen but not thicker, and this appears to be the important dimension in determining the molecule-surface spacing in the low-temperature monolayers. The results presented in this paper show that the large number of cross-sectional areas proposed by other workers for these gases may be a consequence of the changes in packing due to the variable molecular orientation in the monolayer region. In our opinion there is a large number of probable configurations of the adsorbed molecules involving very different orientations with respect to the surface. Furthermore, this is a consequence of the atomic roughness of the model heterogeneous surface considered, and thus the effects should be absent or at least minimized when the adsorbent has a very homogeneous surface. In the case of random atomic surface roughness, it is also necessary to keep in mind that the cross-sectional area can depend on the surface coverage. The configurations analyzed do not show complete tiltangle ordering of the adsorbed molecules at any temperature considered. The tilt-angle distributions of molecules show that in the case of oxygen at low temperatures there is a difference between the first and upper layers which vanishes at temperatures greater than 100 K. The distributions for nitrogen are somewhat narrower than those for oxygen but are otherwise quite similar. Carbon dioxide distributions are wider and present a characteristic (21) Vuong, T.; Monson, P. A. Langmuir, in press.
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not shown by the other gases. The presence of a tail toward higher tilt angles could be due to a combination of the different characteristics of this molecule: shape, size, and quadrupole moment. Although the simulated integral heats of adsorption correspond to what is found in experiments for adsorption on heterogeneous surfaces, the net result of the simulations reported here is to indicate that better models for the isotherms are needed to describe molecular adsorption on atomically rough heterogeneous surfaces. A critical point seems to be the variation of the tilt angle (and thus the effective area occupied) for the adsorbate as the monolayer coverage changes on these surfaces.
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Acknowledgment. L.E.C.d.T. and E.J.B. are researchers of the Comision de Investigaciones Cientificas de la Provincia de Buenos Aires. E.J.B. is Professor of the Universidad Nacional de La Plata (Facultad de Ingenieria). E.J.B. also acknowledges the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET) for financial support under the cooperation agreement between the NSF (U.S.) and CONICET. W.A.S. acknowledges financial support by Grant DMR 902 2681 of the Division of Materials Research of the NSF. LA960246A
